Can 2 raise to the power something be equal to 0? If yes then at what value?

Note by Prabhav Bansal
5 years, 9 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

No.

- 5 years, 9 months ago

No, that's the law of logarithm.

- 5 years, 9 months ago

Can we say 0.0000000000000000000000000000000000000000000001 equal to zero.

- 5 years, 9 months ago

This would only approach 1. Any negative power would be less than 1.

So technically, $2^{-\infty} = 0$. But then again, $-\infty$ isn't a number.

- 5 years, 9 months ago

But still if we say that 2^-100000000000 it is zero.

- 5 years, 9 months ago

No, it's still not absolute zero.

- 5 years, 9 months ago

So, finally we conclude that anything raise to the power any integer is not zero.

- 5 years, 9 months ago

0 raised to the power of any positive real is 0.

You need to qualify what "anything" refers to.

Staff - 5 years, 9 months ago

No. Because 0 is not a number.

- 5 years, 9 months ago

Because 0 is not a number.

Are you sure? xP

I'm guessing you mean infinity?

- 5 years, 9 months ago